In this work, we first study the Floquet two-level system, where the intensity of the probe field has the form of square-wave periodic sequence, which is a basic model of direct frequency comb spectroscopy [1]} and is different from the sine/cosine pulse trains in the Mach-Zehnder interferometer [2]}, [3]}. Note that here the modulation period is shorter than the system's coherence time. We explore the steady excitation probability over a wide driving strength range and give the analytically results with some special scenarios. A lotus-like multi-peak spectrum is observed and the coherent destruction of tunneling effect is found in the strong driving regime. When the Floquet two-level system assisted with a third energy level and a periodically modulated control field, each peak splits into two, resulting in multiple transparency windows. Here the modulation pulse of the control field is the same as that of the probe field, but they are asynchronous. An intriguing finding is that the central transparency window (CTW) in the Floquet three-level system has a similar profile to the traditional EIT or ATS in the un-modulated systems. We use the Akaike information criterion (AIC) method [4]} to discern the CTW from EIT and ATS by evaluating their relative AIC weights for different modulation periods and find that the CTW could be EIT-like or ATS-like in different parameter regimes. Moreover, the quantum interference of the CTW can be modified by the modulation period, which as an additional degree of freedom increases the tunable space of CTW. Therefore, the CTW may provide a superior platform for the explosion of quantum technology than the traditional EIT/ATS.
